Basic Ideas on Fuzzy Plane Geometry

Abstract

Euclidean geometry employs Cartesian coordinate system in which reference axes are perpendicular to each other. In this system every point is represented with a unique tuple which is non-ambiguous. In contrast to classical geometry, the fuzzy geometry deals with the objects with hazy boundary and thus can be viewed as a collection of fuzzy points. In fuzzy set theory it is considered that universe is non-fuzzy, the way we perceive any object is fuzzy or imprecise. This hypothesis guided us to establish fuzzy plane geometry in two dimensional space. This chapter starts with the discussion on reference frame considered for developing fuzzy geometry, which act as a yardstick to measure. The concept of fuzzy point and fuzzy line segment are also introduced here. © 2019, Springer Nature Switzerland AG.